In the case of a known device of this type (CZ 288 848 B6), a first drive unit enables the transfer device to pivot in a reciprocating manner. Furthermore, a second drive unit is provided, the driven shaft of which rotates constantly in the same direction and by means of a pair of cranks in the shape of a parallelogram enables the transfer device to move radially in a reciprocating manner into and out of contact with the hollow glass objects. This device is costly to construct. The device for moving the transfer device horizontally in a linear reciprocating manner requires a large volume of space and has an unfavourably large mass which is to be periodically accelerated and decelerated.